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Fundamentals of Physics

David Halliday, Robert Resnick, Jearl Walker

Chapter 28

Direct Current Circuits - all with Video Answers

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Chapter Questions

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Problem 1

A battery has an emf of $15.0 \mathrm{~V}$. The terminal voltage of the battery is $11.6 \mathrm{~V}$ when it is delivering $20.0 \mathrm{~W}$ of power to an external load resistor $R$. (a) What is the value of $R ?$ (b) What is the internal resistance of the battery?

Yaqub Khan
Yaqub Khan
Numerade Educator
02:33

Problem 2

(a) What is the current in a $5.60-\Omega$ resistor connected to a battery that has a $0.200-\Omega$ internal resistance if the terminal voltage of the battery is $10.0 \mathrm{~V} ?$ (b) What is the emf of the battery?

Suman Saurav Thakur
Suman Saurav Thakur
Numerade Educator
06:27

Problem 3

Two $1.50-\mathrm{V}$ batteries $-$ with their positive terminals in the same direction - are inserted in series into the barrel of a flashlight. One battery has an internal resistance of $0.255 \Omega$, the other an internal resistance of $0.159 \Omega$. When the switch is closed, a current of $600 \mathrm{~m} \mathrm{~A}$ occurs in the lamp. (a) What is the lamp's resistance? (b) What percentage of the power from the batteries appears in the batteries themselves, as represented by an increase in temperature?

Vishal Gupta
Vishal Gupta
Numerade Educator
08:30

Problem 4

An automobile battery has an emf of $12.6 \mathrm{~V}$ and an internal resistance of $0.0800 \Omega$. The headlights have a total resistance of $5.00 \Omega$ (assumed constant). What is the potential difference across the headlight bulbs (a) when they are the only load on the battery and (b) when the starter motor, which takes an additional $85.0 \mathrm{~A}$ from the battery, is operated?

Vishal Gupta
Vishal Gupta
Numerade Educator
02:43

Problem 5

The current in a loop circuit that has a resistance of $R_{1}$ is $2.00 \mathrm{~A}$. The current is reduced to $1.60 \mathrm{~A}$ when an additional resistor $R_{2}=3.00 \Omega$ is added in series with $R_{1}$. What is the value of $R_{1} ?$

Shahab Ullah
Shahab Ullah
Numerade Educator
06:50

Problem 6

(a) Find the equivalent resistance between points $a$ and $b$ in Figure $\mathrm{P} 28.6 .$ (b) Calculate the current in each resistor if a potential difference of $84.0 \mathrm{~V}$ is applied between points $a$ and $b$.

Vishal Gupta
Vishal Gupta
Numerade Educator
02:39

Problem 7

A television repairman needs a $100-\Omega$ resistor to repair a malfunctioning set. He is temporarily out of resistors of this value. All he has in his toolbox are a $500-\Omega$ resistor and two $250-\Omega$ resistors. How can he obtain the de-
sired resistance using the resistors he has on hand?

Vishal Gupta
Vishal Gupta
Numerade Educator
06:41

Problem 8

A lightbulb marked "75 W [at] $120 \mathrm{~V}^{\text {" }}$ is screwed into a socket at one end of a long extension cord in which each of the two conductors has a resistance of $0.800 \Omega$. The other end of the extension cord is plugged into a $120-\mathrm{V}$ outlet. Draw a circuit diagram, and find the actual power delivered to the bulb in this circuit.

Artemisa Maz贸n
Artemisa Maz贸n
Numerade Educator
11:11

Problem 9

Consider the circuit shown in Figure $\mathrm{P} 28.9$. Find (a) the current in the $20.0-\Omega$ resistor and (b) the potential difference between points $a$ and $b .$

Chris Johnson
Chris Johnson
Numerade Educator
04:46

Problem 10

Four copper wires of equal length are connected in series. Their cross-sectional areas are $1.00 \mathrm{~cm}^{2}, 2.00 \mathrm{~cm}^{2}$ $3.00 \mathrm{~cm}^{2}$, and $5.00 \mathrm{~cm}^{2} .$ If a voltage of $120 \mathrm{~V}$ is applied to the arrangement, what is the voltage across the $2.00-\mathrm{cm}^{2}$ wire?

Vishal Gupta
Vishal Gupta
Numerade Educator
05:11

Problem 11

Three $100-\Omega$ resistors are connected as shown in Figure P28.11. The maximum power that can safely be delivered to any one resistor is $25.0 \mathrm{~W}$. (a) What is the maximum voltage that can be applied to the terminals $a$ and $b ?$ (b) For the voltage determined in part (a), what is the power delivered to each resistor? What is the total power delivered?

Shahab Ullah
Shahab Ullah
Numerade Educator
04:54

Problem 12

Using only three resistors $-2.00 \Omega, 3.00 \Omega$, and $4.00 \Omega-$ find 17 resistance values that can be obtained with various combinations of one or more resistors. Tabulate the combinations in order of increasing resistance.

Sophie S
Sophie S
Numerade Educator
03:11

Problem 13

The current in a circuit is tripled by connecting a $500-\Omega$ resistor in parallel with the resistance of the circuit. Determine the resistance of the circuit in the absence of the $500-\Omega$ resistor.

Shahab Ullah
Shahab Ullah
Numerade Educator
07:45

Problem 14

The power delivered to the top part of the circuit shown in Figure $\mathrm{P} 28.14$ does not depend on whether the switch is opened or closed. If $R=1.00 \Omega$, what is $R^{\prime} ?$ Neglect the internal resistance of the voltage source.

Vishal Gupta
Vishal Gupta
Numerade Educator
03:08

Problem 15

Calculate the power delivered to each resistor in the circuit shown in Figure $\mathrm{P} 28.15$.

BN
Braden Nyberg
Numerade Educator
02:26

Problem 16

Two resistors connected in series have an equivalent resistance of $690 \Omega .$ When they are connected in parallel, their equivalent resistance is $150 \Omega$. Find the resistance of each resistor.

Shoukat Ali
Shoukat Ali
Other Schools
08:46

Problem 17

In Figures $28.4$ and $28.5$, let $R_{1}=11.0 \Omega$, let $R_{2}=$ $22.0 \Omega$, and let the battery have a terminal voltage of $38.0 \mathrm{~V} .$ (a) In the parallel circuit shown in Figure $28.5$, which resistor uses more power? (b) Verify that the sum of the power $\left(I^{2} R\right)$ used by each resistor equals the power supplied by the battery $(I \Delta V) .(\mathrm{c}) \mathrm{In}$ the series circuit, which resistor uses more power? (d) Verify that the sum of the power $\left(I^{2} R\right)$ used by each resistor equals the power supplied by the battery $(\mathscr{P}=I \Delta V)$.
(e) Which circuit configuration uses more power?

Vishal Gupta
Vishal Gupta
Numerade Educator
02:08

Problem 18

The ammeter shown in Figure $\mathrm{P} 28.18$ reads $2.00 \mathrm{~A}$. Find $I_{1}, I_{2}$, and $\mathcal{E}$.

Sophie S
Sophie S
Numerade Educator
06:44

Problem 19

Determine the current in each branch of the circuit shown in Figure $\mathrm{P} 28.19 .$

Brandy Heflin
Brandy Heflin
Numerade Educator
09:22

Problem 20

In Figure $\mathrm{P} 28.19$, show how to add just enough ammeters to measure every different current that is flowing. Show how to add just enough voltmeters to measure the potential difference across each resistor and across each battery.

Vishal Gupta
Vishal Gupta
Numerade Educator
09:08

Problem 21

The circuit considered in Problem 19 and shown in Figure P28.19 is connected for $2.00 \mathrm{~min}$. (a) Find the energy supplied by each battery. (b) Find the energy delivered to each resistor. (c) Find the total amount of energy converted from chemical energy in the battery to internal energy in the circuit resistance.

Vishal Gupta
Vishal Gupta
Numerade Educator
09:25

Problem 22

(a) Using Kirchhoff's rules, find the current in each resistor shown in Figure $\mathrm{P} 28.22$ and (b) find the potential difference between points $c$ and $f .$ Which point is at the higher potential?

Vishal Gupta
Vishal Gupta
Numerade Educator
09:55

Problem 23

If $R=1.00 \mathrm{k} \Omega$ and $\mathcal{E}=250 \mathrm{~V}$ in Figure $\mathrm{P} 28.28$, determine the direction and magnitude of the current in the horizontal wire between $a$ and $e$.

Vishal Gupta
Vishal Gupta
Numerade Educator
00:06

Problem 24

In the circuit of Figure $\mathrm{P} 28.24$, determine the current in each resistor and the voltage across the $200-\Omega$ resistor.

Andrija Isakov
Andrija Isakov
Numerade Educator
03:25

Problem 25

A dead battery is charged by connecting it to the live battery of another car with jumper cables (Fig. P28.25). Determine the current in the starter and in the dead battery.

Sophie S
Sophie S
Numerade Educator
07:03

Problem 26

For the network shown in Figure $\mathrm{P} 28.26$, show that the resistance $R_{a b}=\frac{27}{17} \Omega$.

Sophie S
Sophie S
Numerade Educator
04:22

Problem 27

For the circuit shown in Figure $\mathrm{P} 28.27$, calculate (a) the current in the $2.00-\Omega$ resistor and (b) the potential difference between points $a$ and $b$.

Sophie S
Sophie S
Numerade Educator
09:30

Problem 28

Calculate the power delivered to each of the resistors shown in Figure $\mathrm{P} 28.28$.

Vishal Gupta
Vishal Gupta
Numerade Educator
05:15

Problem 29

Consider a series $R C$ circuit (see Fig. $28.16$ ) for which $R=1.00 \mathrm{M} \Omega, C=5.00 \mu \mathrm{F}$, and $\boldsymbol{\varepsilon}=30.0 \mathrm{~V}$. Find
(a) the time constant of the circuit and (b) the maximum charge on the capacitor after the switch is closed.
(c) If the switch is closed at $t=0$, find the current in the resistor $10.0 \mathrm{~s}$ later.

Vishal Gupta
Vishal Gupta
Numerade Educator
03:25

Problem 30

A $2.00-\mathrm{nF}$ capacitor with an initial charge of $5.10 \mu \mathrm{C}$ is discharged through a $1.30-\mathrm{k} \Omega$ resistor. (a) Calculate the current through the resistor $9.00 \mu \mathrm{s}$ after the resistor is connected across the terminals of the capacitor.
(b) What charge remains on the capacitor after $8.00 \mu \mathrm{s}$ ?
(c) What is the maximum current in the resistor?

Sophie S
Sophie S
Numerade Educator
01:35

Problem 31

A fully charged capacitor stores energy $U_{0} .$ How much energy remains when its charge has decreased to half its original value?

Shahab Ullah
Shahab Ullah
Numerade Educator
04:33

Problem 32

In the circuit of Figure $\mathrm{P} 28.32$, switch $\mathrm{S}$ has been open for a long time. It is then suddenly closed. Determine the time constant (a) before the switch is closed and
(b) after the switch is closed. (c) If the switch is closed at $t=0$, determine the current through it as a function of time.

Sophie S
Sophie S
Numerade Educator
09:55

Problem 33

The circuit shown in Figure P28.38 has been connected for a long time. (a) What is the voltage across the capacitor? (b) If the battery is disconnected, how long does it take the capacitor to discharge to one-tenth its initial voltage?

Vishal Gupta
Vishal Gupta
Numerade Educator
03:00

Problem 34

A $4.00-\mathrm{M} \Omega$ resistor and a $3.00-\mu \mathrm{F}$ capacitor are connected in series with a $12.0-\mathrm{V}$ power supply. (a) What is the time constant for the circuit? (b) Express the current in the circuit and the charge on the capacitor as functions of time.

Shahab Ullah
Shahab Ullah
Numerade Educator
03:18

Problem 35

Dielectric materials used in the manufacture of capacitors are characterized by conductivities that are small but not zero. Therefore, a charged capacitor slowly loses its charge by "leaking" across the dielectric. If a certain $3.60-\mu \mathrm{F}$ capacitor leaks charge such that the potential difference decreases to half its initial value in $4.00 \mathrm{~s}$, what is the equivalent resistance of the dielectric?

Vishal Gupta
Vishal Gupta
Numerade Educator
03:30

Problem 36

Dielectric materials used in the manufacture of capacitors are characterized by conductivities that are small but not zero. Therefore, a charged capacitor slowly loses its charge by "leaking" across the dielectric. If a capacitor having capacitance $C$ leaks charge such that the potential difference decreases to half its initial value in a time $t$, what is the equivalent resistance of the dielectric?

Vishal Gupta
Vishal Gupta
Numerade Educator
02:30

Problem 37

A capacitor in an $R C$ circuit is charged to $60.0 \%$ of its maximum value in $0.900 \mathrm{~s}$. What is the time constant of the circuit?

Shahab Ullah
Shahab Ullah
Numerade Educator
03:34

Problem 38

A typical galvanometer, which requires a current of $1.50 \mathrm{~mA}$ for full-scale deflection and has a resistance of $75.0 \Omega$, can be used to measure currents of much greater values. A relatively small shunt resistor is wired in parallel with the galvanometer (refer to Fig. $28.24 \mathrm{a}$ ) so that an operator can measure large currents without causing damage to the galvanometer. Most of the current then flows through the shunt resistor. Calculate the value of the shunt resistor that enables the galvanometer to be used to measure a current of $1.00 \mathrm{~A}$ at fullscale deflection. (Hint: Use Kirchhoff's rules.)

Vishal Gupta
Vishal Gupta
Numerade Educator
02:34

Problem 39

The galvanometer described in the preceding problem can be used to measure voltages. In this case a large resistor is wired in series with the galvanometer in a way similar to that shown in Figure 28.24b. This arrangement, in effect, limits the current that flows through the galvanometer when large voltages are applied. Most of the potential drop occurs across the resistor placed in series. Calculate the value of the resistor that enables the galvanometer to measure an applied voltage of $25.0 \mathrm{~V}$ at full-scale deflection.

Vishal Gupta
Vishal Gupta
Numerade Educator
03:22

Problem 40

A galvanometer with a full-scale sensitivity of $1.00 \mathrm{~mA}$ requires a $900-\Omega$ series resistor to make a voltmeter reading full scale when $1.00 \mathrm{~V}$ is measured across the terminals. What series resistor is required to make the same galvanometer into a $50.0-\mathrm{V}$ (full-scale) voltmeter?

Vishal Gupta
Vishal Gupta
Numerade Educator
02:02

Problem 41

Assume that a galvanometer has an internal resistance of $60.0 \Omega$ and requires a current of $0.500 \mathrm{~mA}$ to produce full-scale deflection. What resistance must be connected in parallel with the galvanometer if the combination is to serve as an ammeter that has a full-scale deflection for a current of $0.100 \mathrm{~A} ?$

Sophie S
Sophie S
Numerade Educator
03:00

Problem 42

A Wheatstone bridge of the type shown in Figure $28.25$ is used to make a precise measurement of the resistance of a wire connector. If $R_{3}=1.00 \mathrm{k} \Omega$ and the bridge is balanced by adjusting $R_{1}$ such that $R_{1}=2.50 R_{2}$, what is $R_{x} ?$

Vishal Gupta
Vishal Gupta
Numerade Educator
08:58

Problem 43

Consider the case in which the Wheatstone bridge shown in Figure $28.25$ is unbalanced. Calculate the current through the galvanometer when $R_{x}=R_{3}=$ $7.00 \Omega, R_{2}=21.0 \Omega$, and $R_{1}=14.0 \Omega .$ Assume that the voltage across the bridge is $70.0 \mathrm{~V}$, and neglect the galvanometer's resistance.

Vishal Gupta
Vishal Gupta
Numerade Educator
07:12

Problem 44

Review Problem. A Wheatstone bridge can be used to measure the strain $\left(\Delta L / L_{i}\right)$ of a wire (see Section $\left.12.4\right)$, where $L_{i}$ is the length before stretching, $L$ is the length after stretching, and $\Delta L=L-L_{i} .$ Let $\alpha=\Delta L / L_{i}$ Show that the resistance is $R=R_{i}\left(1+2 \alpha+\alpha^{2}\right)$ for any length, where $R_{i}=\rho L_{i} / A_{i}$. Assume that the resistivity and volume of the wire stay constant.

Jonathan Ibarra
Jonathan Ibarra
Numerade Educator
03:09

Problem 45

Consider the potentiometer circuit shown in Figure 28.27. If a standard battery with an emf of $1.0186 \mathrm{~V}$ is used in the circuit and the resistance between $a$ and $d$ is $86.0 \Omega$, the galvanometer reads zero. If the standard battery is replaced by an unknown emf, the galvanometer reads zero when the resistance is adjusted to $48.0 \Omega$. What is the value of the emf?

Vishal Gupta
Vishal Gupta
Numerade Educator
11:27

Problem 46

Meter loading. Work this problem to five-digit precision. Refer to Figure $\mathrm{P} 28.46 .$ (a) When a $180.00-\Omega$ resistor is put across a battery with an emf of $6.0000 \mathrm{~V}$ and an internal resistance of $20.000 \Omega$, what current flows in the resistor? What will be the potential difference across it? (b) Suppose now that an ammeter with a resistance of $0.50000 \Omega$ and a voltmeter with a resistance of $20000 \Omega$ are added to the circuit, as shown in Figure P28.46b. Find the reading of each. (c) One terminal of one wire is moved, as shown in Figure $\mathrm{P} 28.46 \mathrm{c}$. Find the new meter readings.

Artemisa Maz贸n
Artemisa Maz贸n
Numerade Educator
03:34

Problem 47

An electric heater is rated at $1500 \mathrm{~W}$, a toaster at $750 \mathrm{~W}$, and an electric grill at $1000 \mathrm{~W}$. The three appliances are connected to a common $120-\mathrm{V}$ circuit.
(a) How much current does each draw?
(b) Is a $25.0-\mathrm{A}$ circuit breaker sufficient in this situation? Explain your answer.

Vishal Gupta
Vishal Gupta
Numerade Educator
03:29

Problem 48

An $8.00$ -ft extension cord has two 18 -gauge copper wires, each with a diameter of $1.024 \mathrm{~mm}$. What is the $I^{2} R$ loss in this cord when it carries a current of
(a) $1.00 \mathrm{~A} ?$ (b) $10.0 \mathrm{~A}$ ?

Vishal Gupta
Vishal Gupta
Numerade Educator
02:54

Problem 49

Sometimes aluminum wiring has been used instead of copper for economic reasons. According to the National Electrical Code, the maximum allowable current for 12 -gauge copper wire with rubber insulation is $20 \mathrm{~A}$. What should be the maximum allowable current in a 12-gauge aluminum wire if it is to have the same $I^{2} R$ loss per unit length as the copper wire?

Vishal Gupta
Vishal Gupta
Numerade Educator
04:31

Problem 50

Turn on your desk lamp. Pick up the cord with your thumb and index finger spanning its width. (a) Compute an order-of-magnitude estimate for the current that flows through your hand. You may assume that at a typical instant the conductor inside the lamp cord next to your thumb is at potential $\sim 10^{2} \mathrm{~V}$ and that the conductor next to your index finger is at ground potential $(0 \mathrm{~V}) .$ The resistance of your hand depends strongly on the thickness and moisture content of the outer layers of your skin. Assume that the resistance of your hand between fingertip and thumb tip is $\sim 10^{4} \Omega$. You may model the cord as having rubber insulation. State the other quantities you measure or estimate and their values. Explain your reasoning. (b) Suppose that your body is isolated from any other charges or currents. In order-of-magnitude terms, describe the potential of your thumb where it contacts the cord and the potential of your finger where it touches the cord.

Eduard Sanchez
Eduard Sanchez
Numerade Educator
02:14

Problem 51

Four $1.50-\mathrm{V}$ AA batteries in series are used to power a transistor radio. If the batteries can provide a total charge of $240 \mathrm{C}$, how long will they last if the radio has a resistance of $200 \Omega ?$

Vishal Gupta
Vishal Gupta
Numerade Educator
11:47

Problem 52

A battery has an emf of $9.20 \mathrm{~V}$ and an internal resistance of $1.20 \Omega$. (a) What resistance across the battery will extract from it a power of $12.8 \mathrm{~W} ?$ (b) a power of $21.2 \mathrm{~W} ?$

Artemisa Maz贸n
Artemisa Maz贸n
Numerade Educator
02:38

Problem 53

Calculate the potential difference between points $a$ and $b$ in Figure $\mathrm{P} 28.58$, and identify which point is at the higher potential.

Sophie S
Sophie S
Numerade Educator
03:17

Problem 54

A $10.0-\mu$ F capacitor is charged by a $10.0-\mathrm{V}$ battery through a resistance $R .$ The capacitor reaches a potential difference of $4.00 \mathrm{~V}$ at a time $9.00 \mathrm{~s}$ after charging begins. Find $R$.

Vishal Gupta
Vishal Gupta
Numerade Educator
04:45

Problem 55

When two unknown resistors are connected in series with a battery, $225 \mathrm{~W}$ is delivered to the combination with a total current of $5.00 \mathrm{~A}$. For the same total current, $50.0 \mathrm{~W}$ is delivered when the resistors are connected in parallel. Determine the values of the two resistors.

Vishal Gupta
Vishal Gupta
Numerade Educator
03:34

Problem 56

When two unknown resistors are connected in series with a battery, a total power $9_{s}$ is delivered to the combination with a total current of $I .$ For the same total current, a total power $\mathscr{P}_{p}$ is delivered when the resistors are connected in parallel. Determine the values of the two resistors.

Shahab Ullah
Shahab Ullah
Numerade Educator
05:36

Problem 57

A battery has an emf $\mathcal{E}$ and internal resistance $r . A$ variable resistor $R$ is connected across the terminals of the battery. Determine the value of $R$ such that (a) the potential difference across the terminals is a maximum,
(b) the current in the circuit is a maximum, (c) the power delivered to the resistor is a maximum.

Ren Jie Tuieng
Ren Jie Tuieng
Numerade Educator
06:58

Problem 58

A power supply has an open-circuit voltage of $40.0 \mathrm{~V}$ and an internal resistance of $2.00 \Omega .$ It is used to charge two storage batteries connected in series, each having an emf of $6.00 \mathrm{~V}$ and internal resistance of $0.900 \Omega .$ If the charging current is to be $4.00 \mathrm{~A},(\mathrm{a})$ what additional resistance should be added in series? (b) Find the power delivered to the internal resistance of the supply, the $I^{2} R$ loss in the batteries, and the power delivered to the added series resistance. (c) At what rate is the chemical energy in the batteries increasing?

Vishal Gupta
Vishal Gupta
Numerade Educator
05:01

Problem 59

The value of a resistor $R$ is to be determined using the ammeter-voltmeter setup shown in Figure $\mathrm{P} 28.59 .$ The ammeter has a resistance of $0.500 \Omega$, and the voltmeter has a resistance of $20000 \Omega$. Within what range of actual values of $R$ will the measured values be correct, to within $5.00 \%$, if the measurement is made using (a) the circuit shown in Figure $\mathrm{P} 28.59 \mathrm{a}$ ? (b) the circuit shown in Figure $\mathrm{P} 28.59 \mathrm{~b}$ ?

Rashmi Sinha
Rashmi Sinha
Numerade Educator
07:51

Problem 60

A battery is used to charge a capacitor through a resistor, as shown in Figure $28.16 .$ Show that half the energy supplied by the battery appears as internal energy in the resistor and that half is stored in the capacitor.

Artemisa Maz贸n
Artemisa Maz贸n
Numerade Educator
07:48

Problem 61

The values of the components in a simple series $R C$ circuit containing a switch (Fig. $28.16$ ) are $C-1.00 \mu \mathrm{F}$, $R=2.00 \times 10^{6} \Omega$, and $\mathcal{E}=10.0 \mathrm{~V}$. At the instant $10.0 \mathrm{~s}$
after the switch is closed, calculate (a) the charge on the capacitor, (b) the current in the resistor, (c) the rate at which energy is being stored in the capacitor, and (d) the rate at which energy is being delivered by the battery.

Artemisa Maz贸n
Artemisa Maz贸n
Numerade Educator
11:13

Problem 62

The switch in Figure P28.62a closes when $\Delta V_{c}>2 \Delta V / 3$ and opens when $\Delta V_{c}<\Delta V / 3 .$ The voltmeter reads a voltage as plotted in Figure $\mathrm{P} 28.62 \mathrm{~b} .$ What is the period $T$ of the waveform in terms of $R_{\mathrm{A}}, R_{\mathrm{B}}$, and $C ?$

Artemisa Maz贸n
Artemisa Maz贸n
Numerade Educator
05:36

Problem 63

Three $60.0-\mathrm{W}, 120-\mathrm{V}$ lightbulbs are connected across a $120-\mathrm{V}$ power source, as shown in Figure $\mathrm{P} 28.63$. Find
(a) the total power delivered to the three bulbs and
(b) the voltage across each. Assume that the resistance of each bulb conforms to Ohm's law (even though in reality the resistance increases markedly with current).

Vishal Gupta
Vishal Gupta
Numerade Educator
07:27

Problem 64

Design a multirange voltmeter capable of full-scale deflection for $20.0 \mathrm{~V}, 50.0 \mathrm{~V}$, and $100 \mathrm{~V}$. Assume that the meter movement is a galvanometer that has a resistance of $60.0 \Omega$ and gives a full-scale deflection for a current of $1.00 \mathrm{~mA}$.

Artemisa Maz贸n
Artemisa Maz贸n
Numerade Educator
12:14

Problem 65

Design a multirange ammeter capable of full-scale deflection for $25.0 \mathrm{~mA}, 50.0 \mathrm{~mA}$, and $100 \mathrm{~mA}$. Assume that the meter movement is a galvanometer that has a resistance of $25.0 \Omega$ and gives a full-scale deflection for $1.00 \mathrm{~mA}$.

Artemisa Maz贸n
Artemisa Maz贸n
Numerade Educator
03:16

Problem 66

A particular galvanometer serves as a $2.00-\mathrm{V}$ full-scale voltmeter when a $2500-\Omega$ resistor is connected in series with it. It serves as a $0.500-\mathrm{A}$ full-scale ammeter when a $0.220-\Omega$ resistor is connected in parallel with it. Determine the internal resistance of the galvanometer and the current required to produce full-scale deflection.

Sophie S
Sophie S
Numerade Educator
02:31

Problem 67

In Figure $\mathrm{P} 28.67$, suppose that the switch has been closed for a length of time sufficiently long for the capacitor to become fully charged. (a) Find the steadystate current in each resistor. (b) Find the charge $Q$ on the capacitor. (c) The switch is opened at $t=0 .$ Write an equation for the current $I_{R_{2}}$ in $R_{2}$ as a function of time, and (d) find the time that it takes for the charge on the capacitor to fall to one-fifth its initial value.

Prashant Bana
Prashant Bana
Numerade Educator
06:52

Problem 68

The circuit shown in Figure $\mathrm{P} 28.68$ is set up in the laboratory to measure an unknown capacitance $C$ with the use of a voltmeter of resistance $R=10.0 \mathrm{M} \Omega$ and a battery whose emf is $6.19 \mathrm{~V}$. The data given in the table below are the measured voltages across the capacitor as a function of time, where $t=0$ represents the time at which the switch is opened. (a) Construct a graph of $\ln (\mathcal{E} / \Delta V)$ versus $t$, and perform a linear least-squares fit to the data. (b) From the slope of your graph, obtain a value for the time constant of the circuit and a value for the capacitance.

Artemisa Maz贸n
Artemisa Maz贸n
Numerade Educator
02:29

Problem 69

(a) Using symmetry arguments, show that the current through any resistor in the configuration of Figure $\mathrm{P} 28.69$ is either $I / 3$ or $I / 6 .$ All resistors have the same resistance $r$. (b) Show that the equivalent resistance between points $a$ and $b$ is $(5 / 6) r$.

Mahipal Kumawat
Mahipal Kumawat
Numerade Educator
03:30

Problem 70

The student engineer of a campus radio station wishes to verify the effectiveness of the lightning rod on the antenna mast (Fig. P28.70). The unknown resistance $R_{x}$ is between points $C$ and $E$. Point $E$ is a true ground but is inaccessible for direct measurement since this stratum is several meters below the Earth's surface. Two identical rods are driven into the ground at $A$ and $B$, introducing an unknown resistance $R_{y} .$ The procedure is as follows. Measure resistance $R_{1}$ between points $A$ and $B$, then connect $A$ and $B$ with a heavy conducting wire and measure resistance $R_{2}$ between points $A$ and $C .$ (a) Derive a formula for $R_{x}$ in terms of the observable resistances $R_{1}$ and $R_{2} .$ (b) A satisfactory ground resistance would be $R_{x}<2.00 \Omega$. Is the grounding of the station adequate if measurements give $R_{1}=13.0 \Omega$ and $R_{2}=6.00 \Omega ?$

Shahab Ullah
Shahab Ullah
Numerade Educator
04:20

Problem 71

Three $2.00-\Omega$ resistors are connected as shown in Figure P28.71. Each can withstand a maximum power of $32.0 \mathrm{~W}$ without becoming excessively hot. Determine the maximum power that can be delivered to the combination of resistors.

Vishal Gupta
Vishal Gupta
Numerade Educator
07:05

Problem 72

The circuit in Figure $\mathrm{P} 28.72$ contains two resistors. $R_{1}=2.00 \mathrm{k} \Omega$ and $R_{2}=3.00 \mathrm{k} \Omega$, and two capacitors, $C_{1}=2.00 \mu \mathrm{F}$ and $C_{2}=3.00 \mu \mathrm{F}$, connected to a battery with emf $\mathcal{E}=120 \mathrm{~V}$. If no charges exist on the capaci- tors before switch $\mathrm{S}$ is closed, determine the charges $q_{1}$ and $q_{2}$ on capacitors $C_{1}$ and $C_{2}$, respectively, after the switch is closed. (Hint: First reconstruct the circuit so that it becomes a simple $R C$ circuit containing a single resistor and single capacitor in series, connected to the battery, and then determine the total charge $q$ stored in the equivalent circuit.)

Vishal Gupta
Vishal Gupta
Numerade Educator
02:20

Problem 73

Assume that you have a battery of $\mathrm{emf} \mathcal{E}$ and three identical lightbulbs, each having constant resistance $R$. What is the total power from the battery if the bulbs are connected (a) in series? (b) in parallel? (c) For which connection do the bulbs shine the brightest?

Vishal Gupta
Vishal Gupta
Numerade Educator